To investigate ferromagnetic semiconductors and insulators, such as the famous EuO, EuS, or CrBr3, we propose a hybridized Kondo-lattice model, where, in addition to the conduction electrons, localized moments (e.g., the 4f-electrons) are modeled as a strongly correlated band system. The quasi-empty conduction band is weakly filled due to the hybridization term. This activates the intraatomic exchange coupling between conduction and localized electrons. Temperature-dependent phase diagrams and quasiparticle densities of states are presented for various coupling and hybridization strengths. Moreover, the influence of the one-particle energy of the localized electrons is discussed. A comparison with mean field calculations is given at the end of this work.